An algebraic approach to the analytic bootstrap View Full Text


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Article Info

DATE

2017-04

AUTHORS

Luis F. Alday, Alexander Zhiboedov

ABSTRACT

We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents. More... »

PAGES

157

References to SciGraph publications

  • 2013-12. The analytic bootstrap and AdS superhorizon locality in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-11. Analytic bootstrap at large spin in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-12. Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents in JOURNAL OF STATISTICAL PHYSICS
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  • 2007-09-11. Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion in JOURNAL OF HIGH ENERGY PHYSICS
  • 2016-05. Causality constraints in conformal field theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-09. Eikonalization of conformal blocks in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-06. Lessons from crossing symmetry at large N in JOURNAL OF HIGH ENERGY PHYSICS
  • 2016-06. Conformal bootstrap with slightly broken higher spin symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-11. Large spin systematics in CFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2016-02. Non-abelian binding energies from the lightcone bootstrap in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-06. Bootstrapping the O(N ) vector models in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-11-09. Comments on operators with large spin in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-12-09. Bounding scalar operator dimensions in 4D CFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-10. Higher-spin correlators in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep04(2017)157

    DOI

    http://dx.doi.org/10.1007/jhep04(2017)157

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1085083906


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